GEOMETRY (Common Core) - NYSED
GEOMETRY (COMMON CORE)
The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (Common Core)
Friday, June 17, 2016 -- 1:15 to 4:15 p.m., only
Student Name:_________________________________________________________
School Name: _______________________________________________________________
The possession or use of any communications device is strictly prohibited when taking this examination. If you have or use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you.
Print your name and the name of your school on the lines above. A separate answer sheet for Part I has been provided to you. Follow the instructions from the proctor for completing the student information on your answer sheet. This examination has four parts, with a total of 36 questions. You must answer all questions in this examination. Write your answers to the Part I multiple-choice questions on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV directly in this booklet. All work should be written in pen, except for graphs and drawings, which should be done in pencil. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. The formulas that you may need to answer some questions in this examination are found at the end of the examination. This sheet is perforated so you may remove it from this booklet. Scrap paper is not permitted for any part of this examination, but you may use the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graph paper is provided at the end of this booklet for any question for which graphing may be helpful but is not required. You may remove this sheet from this booklet. Any work done on this sheet of scrap graph paper will not be scored. When you have completed the examination, you must sign the statement printed at the end of the answer sheet, indicating that you had no unlawful knowledge of the questions or answers prior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer sheet cannot be accepted if you fail to sign this declaration.
Notice... A graphing calculator, a straightedge (ruler), and a compass must be available for you to use while taking this examination.
DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.
GEOMETRY (COMMON CORE)
Part I
Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers on your separate answer sheet. [48]
1 A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which threedimensional object below is generated by this rotation?
Use this space for computations.
(1)
(3)
(2)
(4)
2 A three-inch line segment is dilated by a scale factor of 6 and centered at its midpoint. What is the length of its image?
(1) 9 inches (2) 2 inches
(3) 15 inches (4) 18 inches
Geometry (Common Core) ? June '16
[2]
3 Kevin's work for deriving the equation of a circle is shown below.
x2 4x (y2 20)
STEP 1 STEP 2 STEP 3 STEP 4
x2 4x y2 20 x2 4x 4 y2 20 4 (x 2)2 y2 20 4 (x 2)2 y2 16
In which step did he make an error in his work?
(1) Step 1
(3) Step 3
(2) Step 2
(4) Step 4
Use this space for computations.
4 Which transformation of O?--A would result in an image parallel to O?--A?
y A
x O
(1) a translation of two units down (2) a reflection over the x-axis (3) a reflection over the y-axis (4) a clockwise rotation of 90? about the origin
Geometry (Common Core) ? June '16
[3]
[OVER]
5 Using the information given below, which set of triangles can not be proven similar?
A
R
4 12
S
3 B9CT
(1)
16 H K
G
2
32
8
J
F I
(3)
D
L
M
C
E
N
(2)
Y T
X
Z
R
S
(4)
Use this space for computations.
6 A company is creating an object from a wooden cube with an edge length of 8.5 cm. A right circular cone with a diameter of 8 cm and an altitude of 8 cm will be cut out of the cube. Which expression represents the volume of the remaining wood?
(1) (8.5)3 (8)2(8) (2) (8.5)3 (4)2(8)
(3) (8.5)3 1 (8)2(8) 3
(4) (8.5)3 1 (4)2(8) 3
7 Two right triangles must be congruent if (1) an acute angle in each triangle is congruent (2) the lengths of the hypotenuses are equal (3) the corresponding legs are congruent (4) the areas are equal
Geometry (Common Core) ? June '16
[4]
8 Which sequence of transformations will map ABC onto ABC? y
Use this space for computations.
A A
B
x
C
C
B
(1) reflection and translation (2) rotation and reflection (3) translation and dilation (4) dilation and rotation
9 In parallelogram ABCD, diagonals A?--C and B?--D intersect at E. Which statement does not prove parallelogram ABCD is a rhombus? (1) A?--C D?--B (2) A?--B B?--C (3) A?--C D?--B (4) A?--C bisects DCB.
Geometry (Common Core) ? June '16
[5]
[OVER]
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